I live in East Atlanta and generally drive to the airport, parking at Pre Flight Parking off Camp Springs. They have a 30% off coupon available on their website. I usually park in covered; however, I would expect a 7-day rate with coupon in uncovered to run close to $6/day. I have tried a lot of the parking areas at ATL and Pre Flight is by far my favorite. The parking spots are a bit bigger and more level than most. Shuttle service is good as well. Only considering cost, FastTrack is one of the cheapest.
Although I live close to MARTA, getting to and from there at odd hours with luggage is a challenge. I have yet to find a cab company or shuttle service that is reliable on pickup from my home. One option is to try and get someone to take you to the airport. Once you return to ATL, it is easy to find some sort of transportation to get you home, most likely < $60 for anywhere in metro Atlanta. You can definitely negotiate with the shuttle drivers. For longer personal trips, I sometimes go this route.
Enjoy the trip!